Some properties of reliability, ratio, maximum and minimum in a bivariate exponential distribution with a dependence parameter

Abstract

In this paper, we derived estimators of reliability P (Y < X) and the distribution of ratio in the bivariate exponential density. We also considered the means and variances of M = max {X, Y } and m = min {X, Y }. We finally presented how E(M ), E(m), V ar(M ) and V ar(m) are varied with respect to the ones in the bivariate exponential density.

On the maximum and minimum in a bivariate uniform distribution

“…Woo and Nadarajah (2013) studied maximum and minimum of multivariate Pareto random variables. Lee and Kang (2014) studied some properties for maximum and minimum in a bivariate exponential distribution with a dependence parameter In this paper, we obtain means and variances of max {X, Y } and min {X, Y } in the underlying Morgenstern type bivariate uniform variables X and Y with same scale parameters and different scale parameters respectively. And we obtain the conditional expectations in the underlying Morgenstern type bivariate uniform variables.…”